We can select a single phase space point on each gauge orbit to represent the physical state. We do this by applying gauge conditions. In particular we will consider a canonical gaugeCanonical gauges restrict the phase space variables. Noncanonical gauges [1]} involve the Lagrange multipliers. which takes the form \({\cal G}_a(q,p) \approx 0\)  with \(a = 1,2\) . A good canonical gauge condition must not be gauge invariant, otherwise it would allow more than one point on the gauge orbit to represent the physical state of the system. To be precise, the matrix of Poisson brackets of gauge conditions and gauge generators, \([{\cal G}_a, C_b^{(fc)}]\) , must be nonsingular [1]}.
